The objective of this project is the development and evaluation of statistical methods for use in research related to the Acquired Immunodeficiency Syndrome (AIDS). The particular emphasis will concern statistical modelling of the latency period of infection with human immunodeficiency virus(HIV) using immunologic measurements obtained longitudinally. As an example, hematic monitoring of numbers of CD4 cells in infected individuals over time will be modelled first as a Brownian motion process with negative drift. Within this Brownian motion framework two approaches to the estimation of latency will be investigated. In one approach the expected time required for the number of CD4 cells to drop from normal levels to levels below which symptomatic disease is diagnosed will be calculated as a function of the estimated moments of the Brownian motion process. In the second approach the conditional distribution of the latency period will be estimated, given the first CD4 count after infection. Other immunological measures will be investigated similarly, but will require different modelling assumptions. Simultaneous modelling of several immunologic measures may be required to yield an improved surrogate for the unobserved t\latency. The statistical methods and computer software developed to estimate HIV latency will be evaluated by comparison to actual and simulated a\data for which infection time is known. Of particular importance will be the analysis of data arising from longitudinal studies of HIV infection at New York University Medical Center and the University of Sydney, which have the advantage over simulated data in allowing the direct testing and reformulation of modelling assumptions.